P-Delta Effect
Encyclopedia
In structural engineering
, the P-Δ or P-Delta effect refers to the abrupt changes in ground shear
, overturning moment
, and/or the axial force
distribution at the base of a sufficiently tall structure or structural component when it is subject to a critical lateral displacement
.
The P-Delta effect is a destabilizing moment equal to the force of gravity multiplied by the horizontal displacement a structure undergoes as a result of a lateral displacement.
To illustrate the effect, take the example of a typical statics
case: in a perfectly rigid body
subject only to small displacements, the effect of a gravitational or concentrated vertical load at the top of the structure is usually neglected in the computation of ground reactions
. However, structures in real life are flexible and can exhibit large lateral displacements in unusual circumstances. The lateral displacements can be caused by wind or seismically induced inertial forces. Given the side displacement, the vertical loads present in the structure can adversely perturb the ground reactions. This is known as the P-Δ effect.
In some sense, the P-Delta effect is similar to the buckling load of an elastic, small-scale solid column given the boundary conditions of a free end on top and a completely restrained end at the bottom, with the exception that there may exist an invariant vertical load at the top of the column. A rod planted firmly into the ground, given a constant cross-section, can only extend so far up before it buckles under its own weight; in this case the lateral displacement for the solid is an infinitesimal quantity governed by Euler buckling.
Structural engineering
Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....
, the P-Δ or P-Delta effect refers to the abrupt changes in ground shear
Shearing (physics)
Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It is induced by a shear stress in the material...
, overturning moment
Moment (physics)
In physics, the term moment can refer to many different concepts:*Moment of force is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. A moment is valued mathematically as the product of the...
, and/or the axial force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
distribution at the base of a sufficiently tall structure or structural component when it is subject to a critical lateral displacement
Displacement (vector)
A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P...
.
The P-Delta effect is a destabilizing moment equal to the force of gravity multiplied by the horizontal displacement a structure undergoes as a result of a lateral displacement.
To illustrate the effect, take the example of a typical statics
Statics
Statics is the branch of mechanics concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity...
case: in a perfectly rigid body
Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...
subject only to small displacements, the effect of a gravitational or concentrated vertical load at the top of the structure is usually neglected in the computation of ground reactions
Reaction (physics)
The third of Newton's laws of motion of classical mechanics states that forces always occur in pairs. Every action is accompanied by a reaction of equal magnitude but opposite direction. This principle is commonly known in the Latin language as actio et reactio. The attribution of which of the two...
. However, structures in real life are flexible and can exhibit large lateral displacements in unusual circumstances. The lateral displacements can be caused by wind or seismically induced inertial forces. Given the side displacement, the vertical loads present in the structure can adversely perturb the ground reactions. This is known as the P-Δ effect.
In some sense, the P-Delta effect is similar to the buckling load of an elastic, small-scale solid column given the boundary conditions of a free end on top and a completely restrained end at the bottom, with the exception that there may exist an invariant vertical load at the top of the column. A rod planted firmly into the ground, given a constant cross-section, can only extend so far up before it buckles under its own weight; in this case the lateral displacement for the solid is an infinitesimal quantity governed by Euler buckling.